Patent FR-2,666,946 (U.S. Pat. No. 5,245,647) filed by the applicant discloses a signal sampling device comprising in combination a sigma-delta type oversampling converter associated with a FIR type digital filter performing decimation of successive series of oversamples and a device for synchronizing the samples delivered with an exterior event such as the time of triggering of a seismic source for example. The solution used in this prior device essentially consists in a memory inserted between the sigma-delta converter and the decimation filter, wherein a series of oversamples is permanently stored. On reception of an exterior reference signal, the device is suited to find in the inserted memory the oversamples formed before reception of this signal and to command transfer thereof in the decimation filter so as to produce the first of the resynchronized samples.
Although this solution is perfectly operational, it has the drawback of requiring complex and expensive electronic components inserted between the delta-sigma modulator and the FIR anti-aliasing filter, i.e. a memory and relatively complex means for managing it.
There are also well-known fractional (less than one unit) delay processing techniques notably described by: Laakso T. I. et al : Splitting the Unit Delay; in IEEE Signal Processing Magazine; 1996, allowing to carry out, by means of calculations, time readjustment of the signal sampling. Certain principles thereof, useful for better understanding of the method, are reminded hereafter.
x[n] denotes a series of digitized samples S.sub.k, S.sub.k+1, S.sub.k+2 . . . S.sub.k+p, etc, taken (FIG. 1) from a measuring signal from an initial time t.sub.0 on, with a sampling interval .DELTA.t, by an analog-to-digital converter, and y[n] denotes a series of samples S'.sub.1, S'.sub.2, S'.sub.3 . . . S'.sub.p+1, etc, taken with the same interval from the same measuring signal but readjusted in time from a reference time T.sub.R after t.sub.0. The readjustment time difference D is a positive real number.
This number can generally be written as follows: D=int(D)+d, where int(D) corresponds to a whole number of sampling periods and d is a fraction of a period.
We must have: y[n]=x[n-D].
In order to obtain a delay int(D), it is sufficient to delay the initial signal x[n] by a simple translation. The samples of y[n] are those of x[n] whose index is simply delayed (renumbered) by int(D). The sample bearing number k in the first series for example becomes the sample bearing number 1 in the second series, with k..DELTA.t=int(D). For the fractional part of this time difference, the readjusted samples y[n] will be somewhere between the values of x[n] at two successive sampling positions by the local clock and they must best correspond to the effective amplitudes of the sampled signals at these intermediate positions. This delay with readjustment can be obtained by applying a digital filtering F (FIG. 2).
With the notations specific to the z transform, this delay by digital filtering can be expressed as follows: EQU Y(z)=X(z).z.sup.-D.
The frequency response of the ideal filter H.sub.ID is: EQU H.sub.id =z.sup.-D =e.sup.-j.omega.D
with EQU z=e.sup.j.omega..
The amplitude and phase responses of the ideal filter for any .omega. are therefore: EQU .vertline.H.sub.id (e.sup.j.omega.).vertline.=1
and EQU arg[H.sub.id (e.sup.j.omega.)]=.theta..sub.id (.omega.)=-D.omega..
The phase is often represented as a phase lag defined by: ##EQU1##
a lag that is here D.
The corresponding impulse response is obtained by inverse Fourier transform: ##EQU2##
for any n, hence: ##EQU3##
for any n.
This ideal filter cannot be implemented because its impulse response is infinitely long. There are however several methods allowing to approximate to this ideal solution close enough for the readjustment precision to remain compatible with the precision expected in practice. Selection of the method to be used depends on the specific criteria to be observed within the scope of the application.
The filtering method to be implemented must correspond to certain requirements linked with the means used:passband of the signals to be acquired, sampling frequency, technical limitations of the available digital filtering application means (calculation means) and expected precision of the readjusted sample calculation.
Within the scope of an application to seismic data acquisition for example, it is imposed that the passband of the filter is compatible with all the useful signals carrying seismic information and therefore contains for example the [0 Hz, 375 Hz] frequency interval, as well as a 1000 Hz sampling frequency for the seismic signals. Real-time sample readjustment can be imposed if the acquisition units comprise powerful DSP type signal processors for example, as described in the aforementioned patents, which also contributes to facilitating implementation of digital filtering.